This sounds more like the DNS (domain name server) problem, which occasionally gets reported here, than anything to do with Firefox.
First, find out the addresses of your ISP's domain name servers. There will be two of them (one 'primary' and one 'secondary'), both of which are simply groups of numbers (such as 194.72.6.57). You can find them on your ISP's support pages or, probably, here:
http://www.idl.uk.com/email/isp_settings.htm
or here:
http://www.kitz.co.uk/isp/dns.htm
(If you can't find the addresses, just use those listed for 'OpenDNS' at the bottom of that second link. They'll work with any ISP).
Go into your router's settings. When you look under 'DNS' you'll almost certainly find that the router is set up to allow your ISP's server to automatically assign DNS. Change this to the manual setting, using the strings of numbers from above.
That will probably fix the problem. If not, try reinstalling Firefox. (There's no need to uninstall it first).
Chris